# LLMs for Game Theory: Entropy-Guided In-Context Learning and Adaptive CoT Reasoning

arXiv: https://arxiv.org/abs/2601.10775 · HTML: https://mlsanity.com/paper/2601.10775/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 21 of 21)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Verify-and-Edit: A Knowledge-Enhanced Chain-of-Thought Framework](https://mlsanity.com/paper/2305.03268/) (2023)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness](https://mlsanity.com/paper/2304.10703/) (2023)
- [A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chains](https://mlsanity.com/paper/2402.00559/) (2024)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [RCOT: Detecting and Rectifying Factual Inconsistency in Reasoning by Reversing Chain-of-Thought](https://mlsanity.com/paper/2305.11499/) (2023)
- [Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction](https://mlsanity.com/paper/2406.00755/) (2024)
- [ALYMPICS: LLM Agents Meet Game Theory -- Exploring Strategic Decision-Making with AI Agents](https://mlsanity.com/paper/2311.03220/) (2023)
- [Entropy-based Exploration Conduction for Multi-step Reasoning](https://mlsanity.com/paper/2503.15848/) (2025)
- [Step-by-Step Reasoning to Solve Grid Puzzles: Where do LLMs Falter?](https://mlsanity.com/paper/2407.14790/) (2024)
- [Enhancing the General Agent Capabilities of Low-Parameter LLMs through Tuning and Multi-Branch Reasoning](https://mlsanity.com/paper/2403.19962/) (2024)

## Built on by (most cited first, 1 of 1)

- [What If We Allocate Test-Time Compute Adaptively?](https://mlsanity.com/paper/2602.01070/) (2026)

## Abstract (arXiv)

We propose a novel LLM-based framework for reasoning in discrete, game-theoretic tasks, illustrated with Tic-Tac-Toe. The method integrates in-context learning with entropy-guided chain-of-thought (CoT) reasoning and adaptive context retrieval. The model dynamically adjusts both the number of retrieved examples and reasoning paths according to token-level uncertainty: concise reasoning with minimal context is used when uncertainty is low, whereas higher uncertainty triggers expanded multi-path CoT exploration. Experimental evaluation against a sub-optimal algorithmic opponent shows that entropy-aware adaptive reasoning substantially improves decision quality, increasing the average game outcome from (-11.6%) with the baseline LLM to (+9.5%) with entropy-guided adaptive reasoning over 100 games (win = +1, tie = 0, loss = -1), while maintaining a relatively low number of LLM queries per game. Statistical validation confirms that the improvement is significant, and correlation analysis reveals a negative association between token-level entropy and move optimality. These findings demonstrate that uncertainty-guided adaptive reasoning effectively enhances LLM performance in sequential decision-making environments.